Groupoid C*-Algebras with Hausdorff spectrum

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Abstract

Suppose that G is a second countable, locally compact Hausdorff groupoid with abelian stabiliser subgroups and a Haar system. We provide necessary and sufficient conditions for the groupoid C* -algebra to have Hausdorff spectrum. In particular, we show that the spectrum of C*(G) is Hausdorff if and only if the stabilisers vary continuously with respect to the Fell topology, the orbit space {G}(0) G is Hausdorff, and, given convergent sequences χi → χ and γi ̇ χi →ω in the dual stabiliser groupoid S where the γi G act via conjugation, if χ and ω are elements of the same fibre then χ = ω.

Original languageEnglish (US)
Pages (from-to)232-242
Number of pages11
JournalBulletin of the Australian Mathematical Society
Volume88
Issue number2
DOIs
StatePublished - Oct 1 2013

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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